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CHAPTER 6

VECTOR CONTROL OF DOUBLY FED

INDUCTION GENERATORS

6.1 DESCRIPTION

One of the most recent rotor-side-control schemes is the doubly fed

induction generator. The method uses bi-directional AC-AC converters in the

rotor circuit to control the currents injected into the rotor. The converters,

being bi-directional, can be used to feed the rotor power back to the grid,

reducing rotor power losses and surmounting the main drawback of the rotor

resistance control.

Vector control techniques can be applied to control rotor currents to

achieve fast and decoupled control of the generator (Tapia et al 2003). This

chapter describes the control of doubly fed induction generators using vector

control principles and discusses the effectiveness of the control strategy in

controlling the output power in the presence of disturbances.

6.2 PRINCIPLE OF CONTROL

The control strategy involves the control of the rotor currents to

control the torque and speed of the induction generator, to achieve output

power control. Vector control also enables the decoupled control of stator flux

and electromagnetic torque (Darviersiang et al 2006).

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Doubly fed control methodologies can generally be broken into two

categories: direct torque control and vector control. Direct torque control

(DTC) is a non-linear type of control that operates in a hysterisis manner. It

identifies the state of certain variables, such as flux and torque, and makes a

decision about what rotor voltage to apply to drive the state to a desired value.

A description of DTC for a cage induction machine can be found in

(Nakra et al 1988). The other form of doubly-fed control is vector control,

which is a linear control structure based on simple single input, single output

type controllers (Proportional Integration, for example) or more advanced

state space theory (Yazhou et al 2006). A rotating reference frame is used to

decompose complicated three-phase relationships to orthogonal components.

Vector control is used in this research.

6.3 PRINCIPLE OF OPERATION

The block diagram of the doubly fed generator, operating in the

super synchronous mode is shown in Figure 6.1 (Leonhard 1996 and Liexu

et al 2006). The stator is directly connected to the grid. The rotor is also

connected to the grid but by means of two back-to-back pulse width

modulation converters. The rotor side converter is current controlled to inject

the desired currents into the rotor (Fernando Valenciage 2007).

When the machine is operating in the generating mode, the

mechanical power Pm gets converted into electrical power in the stator (Pstator)

and in the rotor (Protor). The rotor power is processed by the PWM converters

and the grid side converter can be controlled to feed this power as both real

and reactive powers (Pr and Qr) (Rajib Datta et al, 2002). Thus, the induction

generator system is capable of generating a limited amount of reactive power,

unlike the pitch control or rotor resistance controlled wind energy systems.

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The system can usually be made to operate at a unity power factor with a

± 10 % control range on the power factor for the entire system.

Figure 6.1 Structure of the doubly fed induction generator

6.4 DFIG STEADY STATE THEORY

An analytical method for the determination of the steady-state

control laws of the doubly fed induction generators (DFIG) used in wind

turbines is presented. The analytical model is used to derive the converter

control laws of the generator in terms of rotor voltage and control angle (real

and reactive power) overall operation speed range.

The DFIG design it needs suitable compromises between the wind

turbine performance and the respective characteristics of the DFIG, the

gearbox, the static converters and the associated control strategy. The optimal

solution in terms of performance and cost must be derived from global design

approach (Mustafa Kayikci et al 2008).

Pm

DC / AC

AC / DC

Protor

Grid

Pstator

Pr, Qr

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Such an analytical formulation is also very efficient in terms of

execution time and robustness of the global optimization process. The

application of the proposed methodology is illustrated by the study of the

optimal reactive power allocation between the converters, which is an

important design challenge of DFIG system.

Most induction generators in the world are cage-type machines.

Special classes of induction generators with a three-phase wound rotor, called

doubly fed induction generators (DFIG), have become very popular for use as

wind generators as shown in Figure 6.2. These machines usually have a three-

phase inverter connected to the rotor windings, which allows direct control of

the rotor currents. Control of the rotor currents allows for variable speed and

reactive power control.

Figure 6.2 Doubly fed induction generator

A cage-type induction generator draws a fixed amount of reactive

power, which will cause the power factor to be lagging over all operating

conditions. In addition, a cage-type induction machine has a very small speed

range, typically only a few percent variations from the synchronous speed.

DFIG

AC DC

DC AC

DC link Rotor

Stator Grid

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However, direct control of the rotor currents, as allowed by the

DFIG, allow for reactive power control and variable speed operation. A DFIG

can operate at lagging, unity, or leading power factor and can vary its speed

by a much larger margin (usually around 20 to 25 percent above or below the

synchronous speed).

These characteristics make the DFIG ideal for use as a wind

generator. Reactive power control allows a DFIG to help provide voltage

support for the grid, and variable speed operation allows the DFIG to operate

at a higher efficiency over a wide range of wind speeds.

6.4.1 DFIG Steady-State Analysis

The main component of the DFIG system and the conversion chain

is a wind turbine, a gearbox, a DFIG and a four-quadrant power converter.

The DFIG is usually designed with a low pair pole number (two or three) to

obtain acceptable performance in terms of reactive power consumption.

A gearbox is then necessary to adapt the low rotating speed of the wind

turbine (in a range of ~ 10-20 rpm for high-power wind turbines) to the

medium-rotating speed of the DFIG. The power converter is connected

between the grid and the DFIG rotor winding terminals by using slip rings.

The grid side converter (GSC) is usually controlled to operate at unity power

factor and to regulate the DC link voltage.

The rotor side converter (RSC) controls the electrical frequency in

the rotor windings and the real and reactive power flows. The rotor variable

frequency supply allows the variable rotating speed operation of the wind

turbine. Its rotating speed is imposed by the real power flow controlled by the

RSC that is used to provide a suitable torque control loop. The reactive power

managed by the RSC controls the power factor of the whole system, seen by

the grid (GPF) (Aguglia et al 2007).

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6.4.2 The Influences of Model Simplification and Parameters

There has been a fast growing demand for the application of doubly

fed induction generators (DFIG) in wind power plants in recent years. They

have in particular dominated the market in last two years and within

modulation limits, are taken into account in all simulations.

With the envisaged demand and integration of wind power into the

power system, simulation studies and model validation become extremely

important. Currently, the doubly fed induction generator (DFIG) wind

turbines dominate the market due to cost-effective provision of variable-speed

operation. Their ability to control electrical torque and reactive power offer

superior performance concerning system stability. Adequate modeling of

these systems and clear understanding of the effects of different simplification

is paramount if reliable results simulations of power systems with high

penetration of DFIG-based wind plants are sought.

The DFIG mathematical models, as any other mathematical model

of physical device, are simplified either in order to save computational time or

to eliminate the requirement for hard to obtain data. They propose a method to

simplify aerodynamics to represent mechanical power. Modeling of the

aerodynamic efficiency, either Cp has been considered by numerical

approximations or through detailed aerodynamic models of the wind turbine;

however, this influence on transient operation of the DFIG has not been

illustrated (Mustafa Kayikci and Milanovic 2008).

Recently, there has been a growing interest in the use of wind

energy as environmental concerns are on the rise. In spite of this growth,

more technology advances are needed to make wind energy competitive with

many other energy supply methods. Simulation and modeling can be used to

119

study the performance of wind turbine systems (Roohollah Fadaeinedjad et al

2008).

6.4.3 Variable Speed Operation

The aerodynamic theory that justifies the benefit of the variable

speed operation is well described in a number of independent sources. In

short, the aerodynamics of the blades is such that for a particular wind speed,

there is a particular rotational speed that captures the largest amount of power

passing through the swept area.

2 31 2w wP r vπρ= (6.1)

Here ρ is the air density, r is the area radius (blade-length) and Vw

is the wind speed (all in SI units). Not all of this power can be captured by the

wind turbine. The theoretical limit set by Betz’s law (www.windpower.org),

states that the maximum amount of wind power Pw that can be captured by the

turbine is about 59 percent. This amount of available power captured by the

turbine is called the coefficient of power (Cp). The total power capture by the

turbine,

Pt = Pw × Cp

2 31 2t w pP r v Cπρ= (6.2)

Although the theoretical limit is 0.59, in practice most turbines

have a maximum Cp around 0.45. Cp is itself a complicated function of

aerodynamic factors, including the tip speed ratio, and the pitch angle of the

blades (β). To emphasize this, the coefficient of power can be written as Cp.

The tip speed ratio is the ratio of the linear velocity of the turbine blade tip to

the wind speed.

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mech w=r /vλ ω (6.3)

(Please note that outside of this section, the symbol λ will be used for flux

linkages) In equation 6.3 is the rotational speed of the turbine blades.

A series of plots for Cp for different pitch angles is shown in

Figure 6.3. This figure and a very good discussion of this topic can be found

at the Matlab documentation website (www.mathworks.com).

Here it can be clearly seen that for a given pitch angle, there exists

a nominal tip speed ratio (λnom), that maximizes CP(λ, β) and hence maximizes

the power output of the turbine for a given wind speed. Therefore, it is highly

desirable to be able to change the speed of the turbine as the wind speed

changes, such that the turbine maintains the nominal tip speed ratio.

Figure 6.3 Coefficient of power as a function of tip speed ratio and

pitch angle

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For any induction machine, cage or doubly fed type, the steady

state frequency of the rotor currents and voltages will be the slip frequency.

Therefore

mech syn slip syn r2 fω ω ω ω π= − = − (6.4)

In equation (6.4), ωmech is the rotor rotational speed ωsyn is the

synchronous speed and fr is the electrical frequency of the rotor currents and

voltages (all in electrical rad/sec). Here it can be clearly seen that, since the

synchronous speed is fixed by the grid, the rotational speed can be controlled

directly by using the rotor side inverter in Figure 6.2 to force the rotor

currents to a desired frequency.

In practice, the rotational speed of the machine is controlled via

speed and torque control loop cascade structure.

6.4.4 Active and Reactive Power Control

The supervisory control at Wind farm side, to be capable of

providing generating margin from a wind farm, it should be able to receive

operator’s request and distribute power reference signal to each machine for

the desired generation. Further, calculates each machine’s deloaded condition,

come up with a desired generating margin and can be realized by the control

scheme (Michal et al 2006).

Active Power Control of a DFIG, the active power control of a

DFIG is a series of regulating processes between wind turbine and induction

generator. When wind velocity is high enough, the turbine controller regulates

the pitch angle of the turbine blade to ensure the adequate torque for the given

wind power (Le-Ren Chang-Chien et al 2008).

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Another significant advantage of the DFIG is the real and reactive

power control. Note that real power is directly related to the torque and speed

of the generator, so in many ways the issue of real power has already been

addressed in the previous section, although the material presented in this

section offers a different perspective.

A per phase equivalent circuit for a doubly fed induction machine is

shown in Figure 6.4 (Rongve et al 2003 and Riaz 1959). Variables with the

notation denote rotor quantities as seen from the stator side.

Is Ir’

+ Im

Vs

-

Figure 6.4 DFIG per phase equivalent circuit

Some informative relations of a general nature can be seen by

simplifying and neglecting the effects of Rs, jXls and jXlr’. In this case, the per

phase stator and rotor power can be expressed as

*s s s s sS =P +jQ =V I (6.5)

*r r r r rS =P +jQ =V I (6.6)

Assuming a unity turns ratio between the stator and rotor:

V’r = Vr and I’r = -Ir.

+ -

Rs jXls jX’lr

jXm

'rR

s

'rVs

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Then power equations can be written for Figure 6.4. (Note: if there

is a non-unity turns ratio between the stator and rotor, it will not affect the

power equations. Therefore, this analysis is valid for any turns ratio)

2 2* ' ' ' '*

s s r r s m r rV I = I R s + j V X + V I s (6.7)

The active and reactive power is found by taking the real and

imaginary parts of (6.7)

2 2' ' * ' '

r r r rI R s Re I R ss r r rP V I s P s⎡ ⎤= − = −⎣ ⎦ (6.8)

[ ]2 2s m s mV X Im V Xs r r rQ V I s Q s= − = − (6.9)

Since the slips are small, (6.8) and (6.9) illustrate that a small

amount of rotor power yields a large amount of stator power. Therefore, the

DFIG has the effect of amplifying the rotor inverter power. The desired speed

range of the generator is directly related to the power rating of the inverter.

For example, for a DFIG with a plus / minus speed range of 20 percent

(0.2 > s > -0.2), the rotor inverter must be rated for around 20 percent of the

generator rating.

This analysis highlights two of the DFIG’s main advantages. First,

a small amount of reactive power from the rotor becomes a large amount of

reactive power in the stator. Second, the rotor power rating is required to be

only a fraction of the entire generator rating.

A DFIG is a special type of induction generator with a wound rotor.

By proper control of the rotor converter, a DFIG’s can achieve reactive power

control and a wider speed range than for a cage-type induction generator.

Variable speed operation allows the DFIG to capture a greater amount of

power in the wind for a given wind speed.

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There are three main advantages of a DFIG. First, variable speed

operation. Second, a small amount of rotor reactive power becomes a large

amount of stator reactive power. Third, the rotor converter only needs to be

rated for a fraction of the total generator rating.

6.5 dq ANALYSIS FUNDAMENTALS

The time domain voltage, current, and flux linkages equations for a

doubly fed machine are quite complicated. There are three stator windings

and three rotor windings, all linking each other. In particular, the interaction

between the stator and rotor windings is complicated by the linkage being

dependent on the angular position of the rotor. The flux linkage matrix is a

6 × 6 matrix with a dependence on rotor position (Bolik 2004). As an

example, the upper case (example abc) denotes the stator and lower case

(example ABC) denotes the rotor.

( )a a s a mechV i R d dtλ θ= + (6.10)

( ) ( ) ( ) ( )a mech aa ab ac aA mech aB mech aC mechλ θ λ λ λ λ θ λ θ λ θ= + + + + + (6.11)

The symbol λ is used for flux linkage. It is not related to the tip

speed ratio (λ = r ωmech/vw). There are five more sets of equations for the

remainder of the stator and rotor windings.

The flux linkage equation (6.11) is unwieldy in that it has many

terms, half of which have a dependency on the rotor position. The analysis

can be simplified greatly by transforming the three-phase stator and three-

phase rotor (with the rotor angular displacement between them) to a fictional

two-phase stator and two-phase rotor (with no angular displacement), as

shown in Figure 6.5(a) and (b). These two-phase windings are then allowed to

rotate at an arbitrary speed. Often, it is most advantageous to allow the

125

fictional windings to rotate at the synchronous speed. In such a case, the

winding currents will be DC in steady state. There are two ways of creating a

rotating flux: AC currents with fixed windings or DC currents with rotating

windings). These fictional two-phase windings are called d-and q-windings.

(a) (b)

Figure 6.5 (a) Three phase rotor and three phase stator with angular

displacement, (b) Two- phase d and q windings with rotor

and stator aligned

The d and q-axes can be physically considered to be rotatable

orthogonal windings that will produce the same space vector as the fixed

three-phase a, b, and c-windings.

The space vector is a spatially oriented, complex plane

representation of a three-phase quantity.

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Equation (6.12) is a space vector representing the cumulative,

effective current of the three instantaneous phase currents. In this way, a

space vector represents a single, rotatable winding that produces the same

effect as the three fixed windings.

126

Taking this a step further, the real and imaginary parts of the space

vector can be thought of as the current in two stationary orthogonal windings

that produce the space vector. These fictional two-phase fixed windings are

sometimes referred to as “alpha” and “beta” windings. If these windings are

unstuck from their stationary positions, and allowed to rotate or orientate

themselves as the control designer sees fit, they can be called d- and

q-windings.

The d-axis and q-axis stator currents are the (scaled) reflection of

the space vector on the d-axis and q-axis. In Figure 6.6, the scaling factor

is 2 3 , the so-called “power invariant” transformation, because with this

scaling factor a a b b c c sd sd sq sqV i V i V i V i V i+ + = + .

The stator and rotor a-phase, b-phase and c-phase voltage equations

and flux linkage equations can be transformed to the d-axis and q-axis, where

they are much simpler.

Figure 6.6 Space vector reflections on to d – axis and q – axis

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sd sd s sd d sqV i R d dtλ ω λ= + − (6.13)

sq sq s sq d sdV i R d dtλ ω λ= + + (6.14)

rd rd r rd dA rqV i R d dtλ ω λ= + − (6.15)

rq rq r rq dA rdV i R d dtλ ω λ= + + (6.16)

The flux linkage equations are also easily defined, as in

equation (6.17) through (6.20).

( )sd

s

is m sd m rd

i

L L i L iλ = + +14243

(6.17)

( )sq

s

is m rd m rq

i

L L i L iλ = + +14243

(6.18)

( )rd

r

ir m rd m sd

i

L L i L iλ = + +14243

(6.19)

( )rq

r

ir m rq m sq

i

L L i L iλ = + +14243

(6.20)

The most important decision made by the designer implementing

the dq transform is the choice of θ. It is chosen arbitrarily, although some

choices make more sense than others do.

6.5.1 dq Analysis for Non-Unity Turn’s Ratio

For this research and in most practical work, the DFIG will have a

non-unity turns ratio, n. Therefore, the flux linkage equations must include the

turn’s ratio. Also, it will be useful to define the d- and q-axis magnetizing

current.

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md sd rdi i ni= + (6.21)

mq sq rqi i ni= + (6.22)

Including magnetizing current and the turn’s ratio, the flux linkage

equations can be written as:

( )sd

s

is m sd m rd is sd m md

i

L L i nL i L i L iλ = + + = +14243

(6.23)

( )sq

s

is m sq m rq is sq m mq

i

L L i nL i L i L iλ = + + = +14243

(6.24)

( )2rd

r

ir m rd m sd ir rd m md

i

L n L i nL i L i nL iλ = + + = +14243

(6.25)

( )2rq

r

ir m rq m sq ir rq m mq

i

L n L i nL i L i nL iλ = + + = +14243

(6.26)

Only Lm can be considered to be “referred” to the stator. All other

variables are as seen from their respective terminals. For example, Llr is the

rotor leakage inductance as would be measured from the rotor terminal and Irq

is the actual rotor current.

Substituting equation (6.23) through equation (6.26) in the voltage

equation (6.13) through equation (6.16), the resulting equation can be

represented in circuit form, as shown in Figures 6.7, 6.8, 6.9 and 6.10.

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Figure 6.7 d-axis, seen from stator

Figure 6.8 q-axis, seen from stator

Figure 6.9 d-axis, seen from rotor

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Figure 6.10 q-axis, seen from rotor

6.5.2 DFIG Current and Voltage dq Transformer Functions

The standard strategy for DFIG control is to use the rotor d and q-

axis voltage, vrd and vrq, to control the rotor currents, ird and irq. In order to

design the controllers and to gain an understanding of how any of the voltages

affect any of the currents, it is necessary to derive the DFIG current and

voltage transfer functions.

This can be done by substituting equation (6.23) through

equation (6.26) into equation (6.13) through equation (6.16) and rearranging

to get a state equation matrix with currents as the state variables and voltage

as the inputs, resulting in equation (6.27).

[ ] [ ]( , ) ( , )

sd sd sd

sq sq sqd dA d dA

rd rd rd

rq rq rq

i i Vi i Vd A Bi i Vdti i V

ω ω ω ω

⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥= +⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

(6.27)

The A (ωd, ωdA) and B (ωd, ωdA) matrices are dependent on ωd on

ωdA. The dq frame speed, can assumed to be constant. The relative speed of

the dq frame to the rotor contains some mechanical dynamics because it is

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dependent on the rotor speed. However, for the purposes of linearization and

converter control design, the electrical dynamics can be considered much

faster than the mechanical dynamics, and ωdA can be considered constant.

6.6 VECTOR CONTROL

In the stator flux reference frame, simplified equations describing

the dynamics of the induction machine are (Peter Vas 1998)

r r r rs s s s k sV R i d dt jλ ω λ= + + (6.28)

where ωk is the angular speed of the stator flux reference frame. The rotor

voltage equations are not necessary, as the rotor side is current controlled and

the rotor current space vector rir is known.

The stator flux reference frame refers to a reference frame whose

d-axis is aligned along the stator flux space vector. So, by definition,

; 0rs ds qsλ λ λ= = (6.29)

Substituting equation (6.29) into equation (6.28) and separating into

d and q components (Seigfried Heir 2006),

ds s ds sV R i d dtλ= + (6.30)

qs s qs k kV R i ω λ= + (6.31)

since

r r rs s s m rL i L iλ = + (6.32)

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The d and q components of the stator current can be expressed in

terms of the stator flux and the rotor current as

( )qs m s qri L L i= − (6.33)

ds s m dr si L i Lλ= − (6.34)

Substituting equation (6.34) into equation (6.30)

( )k qs s m qr s sV R L i Lω λ= + (6.35)

Substituting equation (6.16) in equation (6.13),

( )s sds s m dr

s

d RV L idt Lλ λ= − − (6.36)

Equation (6.36) expresses the induction machine dynamics in terms

of the input quantities and can be solved to obtain the stator flux linkage

variation. Equation (6.35) is an expression to compute the angular velocity of

the stator flux reference frame, which is used in the conversion from abc to dq

quantities. Since λqs = 0, the electromagnetic torque produced by the machine

can be expressed as

e s qrr

LmT iL

λ= − (6.37)

Thus the stator flux can be controlled by the d- component of the

rotor current and the torque produced can be controlled by the q-component

of the rotor current (Seagay 2005). To enable the control of the flux and the

torque, a stator flux estimate is required, which can compute the torque

produced by the induction generator and estimate rotational speed of the

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stator flux reference frame, using the stator voltages, rotor currents and the

rotor speed as input. The estimator is based on equation (6.28) through

equation (6.37) and the SIMULINK implementation of the estimator is shown

in Figure 6.11 (Rabira and Culloch 2000).

Figure 6.11 Stator flux estimator

6.6.1 Output Power Controller Design

The block diagram of the controller used in the doubly fed

induction generator system is shown in Figure 6.12 (Dalta and Ranganathan

2002). The flux controller, which is shown in Figure 6.12(a), generates the

d-component of the rotor current reference, which is used by the inverter to

control the currents injected into the rotor. Similarly, the speed controller is

used to generate the q-component of the rotor current reference, as shown in

Figure 6.12(b).

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Figure 6.12(a) Flux controller for the doubly fed generator

Figure 6.12(b) Speed controller for the doubly fed generator

The speed reference is generated using the information about the

desired power output and the wind velocity. The speed reference generator is

shown in Figure 6.13. The speed reference generator has two paths, a non-

linear feed forward path and a linear feedback path as in the case of the pitch

control system. The feed forward path computes the power coefficient

required to capture the desired power using,

31

2

refp

w

PC

Avρ= (6.38)

The tip speed ratio is then obtained from a lookup table. The

feedback path compensates for any losses in the system.

135

Figure 6.13 Reference speed generator

The following are the values used for the gains of the P-I

controllers in the simulation.

For the flux controller:

Kp = 10 and Ki = 50.

For the torque controller:

KP = 10 and Ki = 50.

For the speed controller:

Kp = 5 and Ki = 25.

For the power controller:

Kp = 0 and Ki = 1.

The SIMULINK implementation of the system is shown in

Appendix A5.

6.7 RESULTS OF THE SIMULATION

The power output of the system for the wind speed variation is

shown in Figure 6.14. The output power variation is about 2 % and the

settling time is about 5 secs. The system response is fast and the output power

variation is minimal compared to pitch control and rotor resistance control

(Roohollah Fadainedjad et al 2008).

136

Figure 6.14 Output power variation for the DFIG

The rotor speed of the generator is plotted in Figure 6.15. The rotor

speed is also within the limits (10 % of the rated). The rotor power can be fed

back to the grid, thus minimizing losses in the system. Thus, based on our

discussion, comparison between the fixed speed and the variable speed wind

turbines is detailed in Table 6.1.

Figure 6.15 Rotor speed of the induction generator

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Table 6.1 Comparison between various wind turbine systems

Fixed speed Variable speed wind turbine

Squirrel Cage Induction Generator

Synchronous generator Doubly fed induction generator

No Power Electronics Required

Power Electronics required. (100% rating of generator)

Power Electronics required (10 – 40 % rating of machine)

Reactive power support required

Ability to generate reactive power and supply to grid

Ability to generate reactive power and supply to grid

Voltage control not possible

Voltage control possible Voltage control possible

Control of power not possible

Control of active power possible

Control of active power possible

Stall or Active stall control installed

Pitch angle control installed

Pitch angle control installed

Higher vibrations and mechanical stress

Low vibrations and mechanical stress

Low vibrations and mechanical stress

Variations in the wind power are reflected into grid

Wind turbine acts as inertia

Wind turbine acts as inertia

Thus, from Table 6.1, we can see that variable speed wind turbine

with DFIG has several advantages as compared to other types.

6.8 SUMMARY

Vector control is the use of a two-phase transformation to break a

system down into orthogonal components for easier control. For three-phase

machines, this can be seen as the transformation of three-phase real quantities

138

to complex rotating quantities in a fixed frame (space vectors) and then

transformed as orthogonal components in a rotating frame (the d-axis and q-

axis). The d-axis and q-axis, while a fictional mathematical abstraction, can

be thought of in a physical sense as actual rotating windings. This allows an

equivalent, simpler representation of a three-phase machine as a two-phase

machine. Control and analysis can be done more easily, intuitively in degree

frame.

The doubly fed induction generator is found to have the least output

power variation and the fastest response of the three control techniques

simulated. Moreover, the additional complexity of the system enables an

overall system power factor control, to help operate the system at close to

unity power factor.